(a) Is it possible for you to travel far enough and fast enough so that when you
ID: 1912192 • Letter: #
Question
(a) Is it possible for you to travel far enough and fast enough so that when you return from a trip, you are younger than your stay-at-home sister, who was born 5.0 y after you? Yes, provided you travel via a 'wormhole' No, you will always return more than 5.0 y older than her No, you will always return 5.0 y older than her Yes, due to time dilation (b) Suppose you fly on a rocket with a speed v = 0.94c for 8.0 y, according to the ship's clocks and calendars. How much time elapses on Earth during your 8.0 y trip? _____________y (c) If you were exactly 22 y old when you left home and your sister was precicely 17, what are your ages when you return? (Do not round your answers to the nearest year.) your age _____________ y your sister's age _______________ yExplanation / Answer
apparent time = proper time / [square root of (one - v*v/c*c)] a) Yes, due to time dilation b) Flying on a rocket with a speed of 0.94c for 8 y, according to the ship's clock and calendar, we find that v*v/c*c = (0.94)(0.94) = 0.8836 so that 1 - v*v/c*c = 0.1164 and sqrt(1 - v*v/c*c) = 0.3411. Therefore, eight years of proper time gives an apparent time of 23.44 years. 23.44 years elapse on the earth during the 8year trip c) If you were 22y old when you left home, eight years travel time inside the rocket would make you 30 years old at the end of the trip while your 17y-old sister when you left will be (17 years + 23.44 years) = 40.44 years old when you return.
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